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A066389
Number of 2-generated groups of order n: groups that have a generating set of size <=2, i.e., are cyclic or of the form <a,b>.
3
1, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 5, 1, 2, 1, 9, 1, 4, 1, 5, 2, 2, 1, 13, 2, 2, 4, 4, 1, 4, 1, 20, 1, 2, 1, 12, 1, 2, 2, 12, 1, 6, 1, 4, 2, 2, 1, 35, 2, 4, 1, 5, 1, 10, 2, 11, 2, 2, 1, 13, 1, 2, 4, 54, 1, 4, 1, 5, 1, 4, 1, 37, 1, 2, 3, 4, 1, 6, 1, 35, 10, 2, 1
OFFSET
1,4
LINKS
PROG
(GAP)
IsTwoGenerated := function(G) if IsSolvableGroup(G) then return (Length(MinimalGeneratingSet(G)) <= 2); fi; return ForAny(List(ConjugacyClasses(G), Representative), g->ForAny(G, h->Size(Group(g, h)) = Size(G))); end; A066389 := function(n) local count, i; count := 0; for i in [1..NumberSmallGroups(n)] do if IsTwoGenerated(SmallGroup(n, i)) then count := count + 1; fi; od; return count; end; # Eric M. Schmidt, May 02 2013; shortened by Eric M. Schmidt, May 20 2013
CROSSREFS
Cf. A000001.
Sequence in context: A345344 A319004 A234541 * A077191 A317545 A319002
KEYWORD
nonn,nice
AUTHOR
Sharon Sela (sharonsela(AT)hotmail.com), Dec 23 2001
EXTENSIONS
More terms from Reiner Martin, Dec 29 2001
More terms from Eric M. Schmidt, May 02 2013
STATUS
approved